An interpolator is a digital electronic circuit typically used to increase the sampling rate of data. In other words, an interpolator can generate one or more interpolated points between two successive input data points. There are several types of conventional interpolators, such as, for example, finite impulse response (FIR) interpolators, halfband interpolators, cascaded integrator-comb (CIC) interpolators, and polynomial interpolators.
Interpolators are widely used in various signal processing application. For example, U.S. Pat. No. 5,109,481 to Marchetto et al. discloses a system for quadratic and higher order interpolation of pixel color and other pixel values into a bitmap image that enables enhanced shading for generating realistic computer graphics images. U.S. Pat. No. 4,823,000 to Onyon discloses an interpolator for a position encoder, and U.S. Pat. No. 5,063,291 to Buehring discloses an interpolator particularly for use with an optical grating for detecting position in a metrological apparatus. U.S. Pat. No. 5,554,945 to Lee et al. discloses a voltage controlled phase shifter employing a pair of phase interpolators.
The FIR interpolator, for example, is typically used for shaping or filtering a function. Unfortunately, the FIR interpolator usually requires many multipliers and adders, thereby complicating the circuitry and increasing the cost. The CIC interpolator may also require many adders, and full precision is typically required in the integrator section of the circuit. Polynomial interpolators have not achieved widespread use, perhaps due to the popularity of halfband and poly-phase FIR interpolators.
A quadratic interpolator is a form of polynomial interpolator which uses only two multipliers. Quadratic interpolation is performed by fitting a quadratic equation of the form y=b.sub.2 x.sup.2 +b.sub.1 x+b.sub.0 to three known sample points, as disclosed, for example, in U.S. Pat. No. 5,502,662 to Greggain. The patent further discloses quadratic interpolation using reference points determined in such a manner as to eliminate phase distortion and spatial variation. The determination of these reference points uses a linear interpolator for selecting the mid-point between input samples. The interpolated points are used as reference points for a quadratic interpolation where the space between the reference points is one half a distance between respective known sample points.
Unfortunately, a quadratic interpolator may have relatively poor aliasing rejection because only three values are typically used to calculate the quadratic equation coefficients. Other types of interpolators may have better performance, but may require a relatively high degree of circuit complexity, particularly in the number of multiplications and additions that are required.